Book: Why Does E=mc2?

[DeltaV]

Why Does E=mc2 2009 Brian Cox

Came across a recommendation for this book and decided to pick it up. The author does a good job of explaining Einstein's famous equation; I am not
a physicist by any stretch of the imagination, but I found the explanations clear and easy to follow.

I did not realize how much James Maxwell had put into the the foundation of electro-magnetic theory for Einstein to build on (peaked my interest enough that I ordered a book about his work). That, plus a couple of axioms, a thought experiment, a bit of trig and algebra and ... voila! E=mc2! Well, maybe a tiny bit more than that ...

Interesting too how much scientists struggled with the idea of light being a constant speed at the end of the 1800's. And no wonder. Because that means that time ends up being relative.

The only point that I found that is not quite as clear as it could be is why light is squared and not E=mc. I had to do a bit of supplementary research to get that clear in my head (but that might just be me). It is really neat seeing how things all come together with E=mc2 and the formula for kinetic energy (which makes up a part ... a relatively small part ... of the total energy).

And the author explains in the last three chapters why this formula is so important.

Good book if you are interested in fundamental physics.

 

[Ori Vandewalle]

The only point that I found that is not quite as clear as it could be is why light is squared and not E=mc.

Well, for one, that wouldn't have units of energy.

 

[DeltaV]

As I noted in my first comment, I bought a copy of Faraday, Maxwell and the Electromagnetic Field 2014 Nancy Forbes & Basil Mahon. Stuffed it into my backpack on a recent camping trip (now it has the nice smell of campfire smoke).

Enjoyed this book. Part biography, part history of the discoveries that lead to the theory of the electromagnetic field.

Faraday and Maxwell were absolutely brilliant, but each in his own way. Faraday, the son of a poor blacksmith and largely self-taught, became probably the best hands-on experimenter of the nineteenth century, and perhaps of all time. Ah, the time when a person could change the course of science in a homemade lab. We'll never see that again.

And I'll let Einstein himself speak for Maxwell: "One scientific epoch ended and another began with James Clerk Maxwell."

One interesting point related to E=mc2: Henri Poincaré published the formula m=E/c2 several years before Einstein (which I didn't know and this wasn't mentioned in the book Why does E=mc2). Poincaré also wrote that there was no such thing as absolute measures of time and space. But it was Einstein that drew the proper conclusions and packaged everything together in the theory of special relativity. Poor Poincaré. Close but no cigar.

 

[BigBadBob141]

E=mc2, e is energy, m is matter, c is the speed of light in meters per second which is roughly 300,000,000 (about 186,000 miles per second). Basically this means that energy and matter are interchangeable, matter is condensed energy, energy is diffuse matter.
An atomic bomb changes a tiny amount of matter to energy, which means you get a pretty big bang.
The equation means that when an amount of matter is turned into energy the amount of energy you get is the mass of that matter times the speed of light squared, which is roughly 90,000,000,000,000,000 which as numbers go is a little bit on the big side.
So if you had a tiny anti-matter bomb you could really get a big bang (cue manic laughter of mad scientist).
As some modern day submarines are atomic powered and can make their own air and purify water the only limiting factor for staying under water is the amount of food they can carry, their reactors can carry on giving out energy for years and years and years.
P.S. In the equation matter is in kilograms but am damned if I can remember the unit of energy (Joules?), my physics along with my maths is very, very rusty!!!

 

[Ursa major]

The Joule is indeed the unit of energy:

1 Joule = 1 kg m² per s²​

​

(which is how I have to type it as I can't find Verdana's superscript minus sign ).​

 

[Justin Swanton]

So there is something that is common to energy and matter and which can exist as both. I wonder how far it corresponds to Aristotle's Prime Matter, which never exists by itself but always as something else.

 

[Provincial]

I dropped physics after O-level, so forgive my ignorance please when I ask this question: If it is true that c = the speed of light in a vacuum, then presumably it moves at a different speed in an atmosphere, meaning the speed of light is not a constant...? (unless it is the speed of light in a vacuum which is a constant)

 

[Ori Vandewalle]

Yeah, the speed of actual light rays/photons can vary and will be slower in a medium with an index of refraction greater than 1. But "the speed of light" is a fundamental constant of nature and isn't really about light. It's the speed at which all massless particles travel, or the speed of information/causality.

It being a "constant" means you will never measure light to be moving at a different speed because of your reference frame. That is, if a car passes by you doing 60 mph, but you're also in a car going the other direction at 60 mph, you'll measure the first car to be traveling 120 mph. This isn't true of light (or in general when you get up to speeds near c). If you're going 60 past a light ray, you'll still just measure the light ray to be traveling at c, not c+60.

 

[Venusian Broon]

I dropped physics after O-level, so forgive my ignorance please when I ask this question: If it is true that c = the speed of light in a vacuum, then presumably it moves at a different speed in an atmosphere, meaning the speed of light is not a constant...? (unless it is the speed of light in a vacuum which is a constant)

I like to think of what light and a medium really is. Light is an electromagnetic wave and the medium that light passes through are made of particles, like atoms. These particles generally have electric charges, i.e. nuclei have postive charge from their protons and electrons are themselves negative, so they are like a vast field of little dipoles/magnets.

When light passes through a medium, because the photons are EM fields they can* interact with the particles electric and magnetic fields, i.e get scattered, or even be absorbed by the atom, (basically make an electron 'jump' into a higher energy level by absorbing the photons energy, then be re-emitted as the electron drops down back into it's preferred lowest energy state). It is this scattering and interaction that 'slows' down the overall velocity of the macro light wave that we are talking about.

In a vacuum there is nothing for light to interact with, thus it cruises along at velocity c. Note that the light being scattered inside a medium also travels at c in the spaces between atoms or particles, but it is the interactions and scattering that slows it down. Taken to extremes, from memory of my old Physics degree (i.e. I'm probably wrong, it was decades ago ) a photon created in the heart of our Sun is in an environment so densely populated with bits of atoms and electrons that it takes ~10 million years for it to travel to the surface as it is being absorbed/emitted and 'bounced' about so often. As soon as it hits the rarified border of the Sun where the number of particles drops so low that light no longer effectively interacts with them, it then only takes 8 and half minutes to reach a distance equivalent to Earth orbit.

_______________________________________________________

* This will depend on a number of factors such as the wavelength/frequency of the light and the composition of the material. Say for example, the white visible light from the Sun interacts with nitrogen and oxygen in our atmosphere mainly in the blue end of the spectrum, thus making our sky blue, but the red end is much less scattered. Other wavelengths like 1m wavelength radio waves don't interact at all with anything in our atmosphere and just pass through uninterrupted and we can detect them on the ground.

 

[Ori Vandewalle]

Taken to extremes, from memory of my old Physics degree (i.e. I'm probably wrong, it was decades ago ) a photon created in the heart of our Sun is in an environment so densely populated with bits of atoms and electrons that it takes ~10 million years for it to travel to the surface as it is being absorbed/emitted and 'bounced' about so often.

I remember the figure being in the neighborhood of 10 or 100 thousand years. But it's a very approximate thing of course, and the derivation is always based on a very hand-wavey random walk+mean free path picture.

 

[BigBadBob141]

REF: Provincial.
You are quite right, I should have said the speed of light in a perfect vacuum that is a constant, it does slowdown a bit in glass, water, air ect.
There is even a type of radiation called Cherenkov radiation, where you have radioactive elements stored in water, if you look down in to the storage tank you can see a blue glow, this is caused by atomic particles given off by the stored material that are traveling faster then the speed of light in water!
P.S. See the short story "Light Of Other Days" by I think Bob Shaw, in which a material called slow glass slows light so much it takes years for it to traverse a pane of it.
P.P.S. Oh boy do I hate auto bl***y correct!!!!!

 

[Provincial]

REF: Provincial.
You are quite right, I should have said the speed of light in a perfect vacuum that is a constant, it does slowdown a bit in glass, water, air ect.
There is even a type of radiation called Cherenkov radiation, where you have radioactive elements stored in water, if you look down in to the storage tank you can see a blue glow, this is caused by atomic particles given off by the stored material that are traveling faster then the speed of light in water!
P.S. See the short story "Light Of Other Days" by I think Bob Shaw, in which a material called slow glass slows light so much it takes years for it to traverse a pane of it.
P.P.S. Oh boy do I hate auto bl***y correct!!!!!

Physics, especially this stuff, always sounds amazingly cool (when you aren’t expected to understand the maths)! And yes, I remember that story, with the glass causing car accidents when used as a windscreen, before it’s properties were understood, and also being a silent witness to crimes when it was used for street lighting. Great stuff!

 

[mosaix]

Many years ago, and I’ve never been able to find it since, I read that the speed of light in the formulae was just there to represent ‘a very big number’ and it was not actually the speed of light.

Is that true or did I just dream it?

 

[Venusian Broon]

Many years ago, and I’ve never been able to find it since, I read that the speed of light in the formulae was just there to represent ‘a very big number’ and it was not actually the speed of light.

Is that true or did I just dream it?

I'm not sure this is what you read but...

...Maxwell applying his famous equations in a region with no charge and no currents, derviving two differential equations where c is defined as equal to (mu_0 x epsilon_0) ^ (-1/2). And mu_0 is the permeability of free space and epsilon_0 is the permittivity of free space and are constants (who appear in Maxwell's 4th equation).

The value of these EM constants were known, as was the speed of light and the fact that these two EM constants derived the speed of light in this formula from his equations made Maxwell propose that light and radio waves were propagating electromagnetic waves.

When light goes through a medium then the phase velocity of light includes the relative permeability and permittivity. (Look up Wikipedia if interested, but they are factors that multiple the free space constants.)

So c there appears as a constant in a pair of differential equations.

Might it be that you are remembering?

 

[mosaix]

Thanks for that, VB.

That’s all way above my pay grade I’m afraid so definitely not.